LC resonance, Q factor & bandwidth worksheet with answers

Free printable LC resonance, Q factor & bandwidth worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
tvC​iL​T/4T/2TV0​ = 24 VC = 470 nF

A 470 nF capacitor is charged to 24 V and then connected to an ideal 47 mH inductor. Find the total energy W that swings between them, in µJ.

C = 470 nFV0 = 24 VL = 47 mH
W = µJ
2.Easy
f|I|0.70712 kHzf1​f2​BW = 80 Hz

A resonance curve peaks at 2 kHz, and its half-power points are 80 Hz apart. Find the quality factor Q.

f0 = 2 kHzBW = 80 Hz
Q =
3.Medium
V1 kΩ10 µH22 nF

A parallel RLC circuit has R = 1 kΩ, L = 10 µH and C = 22 nF. Find its quality factor Q.

R = 1 kΩL = 10 µHC = 22 nF
Q =
4.Medium
V10 Ω100 µH22 nF

A series RLC circuit has R = 10 Ω, L = 100 µH and C = 22 nF. Find its bandwidth BW in kHz.

R = 10 ΩL = 100 µHC = 22 nF
BW = kHz
5.Hard
V50 ΩLC = ?

Design a series RLC filter with a total resistance of 50 Ω, a resonance frequency of 200 kHz and a bandwidth of 8 kHz. Find the capacitance C in nF.

R = 50 Ωf0 = 200 kHzBW = 8 kHz
C = nF
6.Hard
f|I|0.7071f0​ = ?400 kHz480 kHzBW

The half-power frequencies of a resonance curve are 400 kHz and 480 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 400 kHzf2 = 480 kHz
Q =

Answer key

  1. 1. W = 135.4 µJ
  2. 2. Q = 25
  3. 3. Q = 46.9
  4. 4. BW = 15.92 kHz
  5. 5. C = 0.6366 nF
  6. 6. Q = 5.477

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